7.1 CONCLUSIONS
The main conclusions drawn from the programme o f work reported in this thesis are as follows:
• The FE technique can be used to investigate the temperature response of brake discs
during the brake application and subsequent cooling period. However, the validity of the results is dependent on how faithfully the physical boundary conditions and material properties are represented in the analysis.
• Elastic stress analysis was unable to accurately predict the thermal stress response of
brake discs because the high temperature gradients during severe brake applications resulted in high thermal stresses beyond the yield strength of the material. However, elastic analysis can be used to investigate the deformations of brake discs under thermal loading. These vary according to the brake disc geometry: a back-vented design provided a much lower degree of disc coning than the corresponding front- vented design but at the expense of higher thermal stresses.
• The monotonic stress-strain curves of the cast iron material from the Rover brake
disc became non-linear at low strains indicating plasticity and voiding within the material. Furthermore, they were different in tension and compression and quite sensitive to temperature, particularly as the temperature was raised above 300°C. The effect of cyclic loading on the brake disc cast iron specimens has also been investigated at a variety of temperature conditions. The cast iron material also
Chapter 7 Conclusions and Future Work
C h apter 7 C onclusions an d Future Work
displayed cyclic hardening in compression and cyclic softening in tension. Fracture occurred at lower strains in comparison with these under monotonic loading at the same temperature.
• The standard cast iron material model in the widely-used commercial FE package
ABAQUS can be used to investigate the stress response of materials that have different stress-strain behaviour in tension and compression. However, this material model used a Rankine yield criterion for yield in tension and a standard von Mises criterion in compression together with non-associated plastic flow rules. Moreover, the equivalent plastic strain in tension is directly related to the associated plastic strain in compression and vice versa. This is despite the fact that the mechanisms for inelastic straining in tension and compression are different due to the effect of the opening and closing o f gaps between the graphite flakes and metal matrix. Therefore, this material model is unsuitable for estimating the plastic strain accumulation under cyclic loading in the disc brake thermal stress analysis.
• Based on the assumption o f independent plastic strain mechanisms in tension and
compression, a user-developed subroutine material model has been developed to represent the cast iron properties with different yield strengths in tension and compression which were also a function o f temperature. Furthermore, both tensile and compressive yield surfaces used the von Mises stress criterion with the associated flow rule in order to simplify the material model. In order to provide a smooth transition between tensile and compressive yield regimes, a linear transition zone of 30 M Pa hydrostatic pressure has been determined as being near optimum in terms o f providing numerical robustness with minimal loss of accuracy of strain prediction.
C h apter 7 C onclusions an d Future Work
•
The application of the user-developed subroutine material model to the back- andfront-vented disc models is more realistic in terms of tensile and compressive plastic strain accumulations. The results indicated that a high compressive plastic strain occurred at the inboard rubbing surface during the brake application for the back- vented disc and at the outboard rubbing surface for the front-vented disc. Moreover, cyclic plastic strain reversals between tension and compression were found at the inner radius of the long vane for the back-vented disc and at the neck area for the front-vented disc. Based on the maximum plastic strain accumulation, the back- vented disc would experience cracking at the inner radius of the long vane with fewer thermal cycle than the front-vented disc for which cracking would occur at the neck area.
• It is thought that the user-developed cast iron material model will find application in
the analysis of thermal stress and plastic strain accumulation associated with a wide variety of cast iron components such as, for example, engine blocks and cylinder heads. Furthermore, its use need not be restricted to automotive components.
7.2 FUTURE WORK
There is significant scope for further work and this is summarised below:
• A full 3D analysis of the brake disc including the pads should be considered in order
to investigate the effects of rotating heat source and the non-uniform heat flux over the rubbing surfaces due to non-uniform pressure distributions.
• It has not been possible to determine the monotonic and cyclic stress-strain curves on the cast iron material between 25-300°C because of the limitation o f the induction heating system. It is important that this is obtained because of the high temperature gradients found during the brake application. Also, the yield surface of cast iron when subject to biaxial loads should be investigated in order to study its anisotropic yield behaviour in tension and compression.
• The fatigue behaviour of the brake disc cast iron material should be investigated
over a range of cyclic strain amplitudes in order to predict the fatigue life. Furthermore, the effect of different strain amplitudes in tension and compression should be considered since the damage mechanisms are different.
• M odifying the user-developed subroutine material model for cast iron should be
considered in order to simulate the effect of void growth on the yield surface in tension by, for example, the adoption of a Gurson-type yield criterion and associated void growth law [42,43]. In addition, the cyclic softening in tension and hardening in compression should be taken in account.
• A programme of experimental work needs to be undertaken using a full size
dynamometer since it can subject the brake to the same sequence of high energy stops that has been modelled in the numerical simulation. This will provide the necessary data needed to validate the model and provide an indication of the location of possible fracture sites.
REFERENCES
[1]
M etzler, H., 'The Brake Rotor -Friction Partner o f Brake Linings',
SAETechnical Paper Series: 900847, 1990
[2]
Angus, H. T., Lam b A. D. and Scholes J. P., 'Conditions Leading to Failure in
Cast Iron Brakes',
BICRA Journal, Vol. 14, No. 4, pp 371-385, 1966[3]
L im pert, R., 'An Investigation o f Thermal Conditions Leading to Surface Rupture
o f Cast Iron Rotors',
SAE Technical Paper Series: 720447,1972[4]
Rainbolt, J. D., 'Effect o f Disk Material Selection on Disk Brake Rotor
Configuration',
SAE Technical Paper Series: 750733,1975[5]